Community Preserved Social Graph Publishing with Node Differential Privacy

The goal of privacy-preserving social graph publishing is to protect individual privacy while preserving data utility. Community structure, which is an important global pattern of nodes, is a crucial data utility as it serves as fundamental operations for many graph analysis tasks. Yet, most existing methods with differential privacy (DP) commonly fall in edge-DP to sacrifice security in exchange for utility. Moreover, they reconstruct graphs from the local feature-extraction of nodes, resulting in poor community preservation. Motivated by this, we propose PrivCom, a strict node-DP graph publishing algorithm to maximize the utility on the community structure while maintaining a higher level of privacy. Specifically, to reduce the huge sensitivity, we devise a Katz index-based private graph feature extraction method, which can capture global graph structure features while greatly reducing the global sensitivity via a sensitivity regulation strategy. Yet, with a fixed sensitivity, the feature captured by Katz index, which is presented in matrix form, requires privacy budget splits. As a result, plenty of noise is injected, thereby mitigating global structural utility. To this end, we design a private Oja algorithm approximating eigen-decomposition, which yields the noisy Katz matrix via privately estimating eigenvectors and eigenvalues from extracted low-dimensional vectors. Experimental results confirm our theoretical findings and the efficacy of PrivCom.